Electromagnetic Induction

Step 1: Understanding the induced EMF.
As the loop moves with a constant velocity, the magnetic flux through the loop changes due to the changing distance from the current-carrying wire. According to Faraday's law of induction, an EMF is induced in the loop. The induced EMF depends on the distance from the wire and the velocity .
Step 2: Using the formula for induced current.
The induced current in the loop is given by , where is the permeability of free space, is the current in the wire, and is the resistance of the loop.
Step 3: Conclusion.
Thus, the correct answer is option (C).

Step 1: Understanding the mutual inductance.
For two co-planar coils, the mutual inductance depends on the geometrical configuration of the coils. It is proportional to the square of the radius of the larger coil and inversely proportional to the radius of the smaller coil , assuming . This relationship can be derived from the formula for mutual inductance in terms of coil radii.
Step 2: Conclusion.
The correct answer is option (C) because the mutual inductance is proportional to .